2017/10/12 by Hüseyi̇n Çakallı, Cakalli, Huseyin
Decision Sciences · Mathematics · #26A15 #40A05 #40A30 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.1710.04405
openalex publication_date 2017/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a concept of statistically p-quasi-Cauchyness of a real sequence in the sense that a sequence (αk) is statistically p-quasi-Cauchy if limn→∞(1)/(n)|\k≤ n: |αk+p-αk|≥ε\|=0 for each ε>0. A function f is called statistically p-ward continuous on a subset A of the set of real umbers ℝ if it preserves statistically p-quasi-Cauchy sequences, i.e. the sequence f(x)=(f(αn)) is statistically p-quasi-Cauchy whenever \boldsymbolα=(αn) is a statistically p-quasi-Cauchy sequence of points in A. It turns out that a real valued function f is uniformly continuous on a bounded subset A of ℝ if there exists a positive integer p such that f preserves statistically p-quasi-Cauchy sequences of points in A.